Adaptive harmonic balance method for nonlinear time-periodic flows

An adaptive harmonic balance approach is developed and applied to a supersonic/subsonic diverging nozzle subject to unsteady periodic outflow conditions. The adaptive method minimizes the computational work required to obtain the harmonic balance solution by augmenting the frequency content in each cell as required to capture the local flow physics. Augmentation automatically adjusts with grid density, resulting in lower frequency content on coarse grids. The new adaptive harmonic balance method produces solutions equivalent to a non-adapted harmonic balance solutions, but with up to an 86% reduction in computational effort.